Answer:
(a) Not independent
(b) The probability the woman has a Bachelor's Degree and has never married is 0.046.
Explanation:
Denote the events as follows:
X = American women aged 25 years or older have a Bachelor's Degree
Y = American women aged 25 years or older have never married
The information provided is as follows:
P (X) = 0.202
P (Y) = 0.165
P (X | Y) = 0.228
P (Y | X) = 0.186
(a)
If two events, say A and B are independent then,
P (A|B) = P (A) and P (B|A) = P (B)
Since,
P (X | Y) ≠ P (X)
P (Y | X) ≠ P (Y)
The events "have a Bachelor's Degree" and "never married" are not independent.
(b)
Compute the probability the woman has a Bachelor's Degree and has never married as follows:

Thus, the probability the woman has a Bachelor's Degree and has never married is 0.046.